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Evolution in Structured Populations

Why reductionism doesn’t work, Part 2: Groups to individuals

Williams (1966) famously wrote “In explaining adaptation, one should assume the adequacy of the simplest form of natural selection, that of alternative alleles in Mendelian populations, unless the evidence clearly shows that this theory does not suffice.” This principle of parsimony makes two interesting points. The first phrase “In explaining adaptation” makes the point that Williams was interested in examining patterns, and then using those patterns to infer how selection acted in the past. This is very different than modern MLS approaches in which the process of selection is examined. This is why parsimons (A bit of artistic license with the spelling) are so unimportant in modern MLS theory: such rules are not necessary if you are studying the process rather than inferring the process from standing patterns. More importantly, this principle implies that group selection can in many cases be reduced to individual selection, or even genic selection. The only thing that stands in the way of doing this is the ecology. Unless the trait is “altruism”, and thus impossible to evolve at a lower level, there is no reason not to act as if it was one of these lower levels of selection.

But is this really true? Last week I discussed why individual selection can’t be reduced to genic selection. It turns out that the situation is worse trying to reduce group to selection on the underlying individuals. So with that long-winded introduction out of the way, the main reason that group selection cannot be reduced to individual selection is indirect genetic effects (IGEs). Indirect genetic effects occur when genes in one individual affect the phenotype of another individual.

This is an effect that has been seen time and time again. The most aggressive chickens lay the most eggs, but also suppress the egg laying of their cage mates (Muir 1996, Poultry Science 75:447), crop plants aggressively interact such that the highest producing plants most strongly suppress their neighbors (Griffing 1977 in: Proceedings of the International Congress on Quantitative Genetics, August 16-21, 1976.) and many more examples. The important thing is that interactions that are internal to the unit of selection can contribute to the response to selection, whereas if they are external to the unit they cannot. Thus group selection can act on IGEs, but individual selection cannot.

To see this it is easiest to use the Price equation. The Price equation divides the covariance between a trait and relative fitness into within and between group components. It is easy and convenient to use this partitioning to make the point I want to make, but it is important to emphasize that the Price partitioning should never be equated with group and individual selection (Are you listening West and Gardner?).

Imagine we have a metapopulation in which individuals interact within groups but not between groups. The individuals interact in some manner that affects all individuals in the group in the same way. That is, perhaps they release waste products into their environment and everybody gets equally poisoned, or on a more positive note, perhaps they release some chemical public good. Further imagine that we have a trait, z, that is influenced by direct genetic effects (DGE), indirect genetic effects (IGE) and environmental effects. Thus, the trait value of the ith individual in the jth deme is:

Zij = DGEij + IGE.j + eij

Further imagine that the fitness of the ijth individual relative to the metapopulation mean fitness is wij, and the correlation between environmental effects and fitness is zero (just to get them out of the way).

To bring this back to my posts on Gardner, if I was following his model, at this point what I would want to do is partition the “total breeding value” so I could compare it with his partitioning of Fisherian breeding values. “Breeding value” is defined by Fisher (1930, Falconer and MacKay 1996) to be the average value of an individual’s offspring measured as a deviation from the population mean. This breeding value assumes that there is no population structure and that offspring interact randomly with other individuals in the population. Because they ignore population structure Fisherian breeding values cannot be partitioned. Bijma and Wade (2008. JEB 21: 1175-1188) solved this by defining “Total Breeding Value” to be the average value of an individual’s offspring measured in their native social environment as a deviation from the metapopulation mean. Unlike Fisherian breeding values, total breeding values can be partitioned. If you prefer to partition total breeding values replace “z” with total breeding value in the equation below, and replace DGE’s and IGE’s with their additive genetic equivalent.

If we put all this together, using the Price equation to partition the covariance between total breeding value and relative fitness we get an algebraic explosion!

Or much more simply:

So, in words, this simply tells us that the within demes covariance between phenotype and relative fitness (red in the equation) includes ONLY direct genetic effects, whereas the between demes covariance between phenotype and relative fitness (blue in the equation) includes both direct and indirect genetic effects. This is shown graphically in the following figure:

The sources of variation for a trait and the group mean of the trait. For clarity I have left the total variance proportions the same for the group mean trait, even though in most situations the direct genetic effects and the environmental effects would be reduced due to averaging. Although the genetic components underlying the trait are unchanged by taking the average, the heritable component does change. For the individual trait only the direct effects are heritable, whereas for the group mean trait both the direct and indirect genetic effects are heritable.

What this is saying is that from an evolutionary perspective a trait and the group mean of a trait are actually different traits. Because group selection can act on both direct and indirect effects it can produce genetic changes that are qualitatively different than selection acting on the individual level. As I have pointed out numerous times this is not a minor theoretical issue that experimentalists can ignore. Indirect genetic effects have shown up as major factors in the response to group selection in every situation where it has been possible to infer there presence, including both experiments specifically designed to detect them (e.g., Goodnight 1990 Evolution 44:1625), or where it was obvious even though the experiment did not have explicit treatments to detect them (e.g., Muir 1996).

Next week, as promised for this week, but not delivered: Why reductionism does work.